Verify that A(adj A) = (adj A) A = IAI·I for the matrix A = \(\begin{bmatrix}2 & 3 \\-1 & 4\end{bmatrix}\)

It the letters of the word are arranged as in dictionary, find the rank of the word "AGAIN".

A point moves so that its distance from the point (-1, 0) is always three times its distance from the point (0, 2). Find its locus.

Prove that\(\left\{1+\cot x-\sec\left(\frac{\pi}{2}+x\right)\right\}\left\{1+\cot x+\sec\left(\frac{\pi}{2}+x\right)\right\}=2\cot x\)

Is the function defined by f(x) = x² -sin x + 5 is continuous at x =\(\pi\)?

Separate the intervals in which the function x³ + 8x² + 5x - 2 is increasing or decreasing.

If I deposit Rs.500 every year for a period of 10 years in a bank which gives C.I 5% per year, Find out the amount I will receive at the end of 10 years

Events A and B are such that P(A)=\(\frac { 1 }{ 2 } \), P(B)=\(\frac { 7 }{ 12 }\), and P(not A or not B) = \(\frac { 1 }{ 4 }\), state whether A and B are independent?

Calculate the correlation co-efficient from the below data:

X	1	2	3	4	5	6	7	8	9
Y	9	8	10	12	11	13	14	16	5

prove that the correlation co-efficient is the geometric mean of regression co-efficients.